JPH08285572A - Method for evaluating shape of sheet - Google Patents

Abstract

PURPOSE: To obtain a proper evaluation data in the controlling of a shape based on an evaluation index by performing an approximation for a degree of steepness measuring data measured by a curve according to a polynomial of four orders or more to accomplish the evaluation of the shape accurately. CONSTITUTION: The degree of width-wise steepness measured data of n measured by a shape detector are used to perform an approximation according to a polynomial of specified four or six orders. In the converting of the resulting coefficient to a shape evaluation index, a peak value of a shape is defined as an equivalence peak value, as viewed from a relationship of the peak value and an effective value when the shape is regarded as comprising a sine wave or a synthetic wave containing a higher order component. Then, symmetrical components and non-symmetrical components are plotted on an evaluation plane to evaluate the shape from the length and the phase of a vector. This enables accurate evaluation of the deficiency in the shape as caused in the actual process even when the shape is complicated thereby obtaining an evaluation index corresponding even to an evaluation method in off line as in the past.

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention measures the shape of a product with a shape detection device in the process of continuously manufacturing a strip-shaped material regardless of metal or non-metal, and evaluates the characteristics of the shape of the product.
Alternatively, the present invention relates to a method for comprehensively evaluating shape data represented by a steepness or a tension deviation value obtained from a shape detection device as some feature quantities when performing shape control based on an evaluation index. .

[0002]

2. Description of the Related Art In an intermediate or finishing process in which a strip-shaped metal material such as iron or aluminum or a strip-shaped non-metal material such as a film or paper (collectively referred to herein as "thin plate") is continuously processed and manufactured, A shape detection device is installed in the process, the shape is continuously measured online, and the measured value is observed to grasp the processing status, prevent product abnormalities, and have a control means. In this case, the shape control actuator is manually or automatically adjusted to control the product shape to a target shape.

As a method of measuring the shape, generally, a tension is applied to the material being processed and a defective shape is latent, so that a method of measuring the tension distribution in the width direction and converting it into the shape is adopted. The evaluation of the shape in the stage of secondary processing of the material is evaluated by the steepness under the tension release, and therefore the measured value of the tension distribution is converted into the steepness. The steepness is obtained as n discrete values when the shape measuring device is equipped with n tension measuring sensors.

In the case of a shape detecting device which is practically used,
Since the value of n is generally a large value of 16 or 32 or more, it is not a good idea to use this measured value as it is for evaluation and control, and since the measured value always contains noise, statistically Need to be evaluated. As a known method of statistically evaluating, a method of approximating a fourth-order polynomial is generally adopted. In addition to the polynomial approximation, various methods such as a method of approximating a trigonometric function and a method of using an orthogonal function have been proposed. However, since the polynomial approximation is the simplest, it is highly practical and is currently generally applied.

In polynomial approximation of the steepness measurement data measured in the width direction, x _k (│x _k │≤1) (k = 1,2, ... n) is set to the position where the sensor is installed. The dimensionless normalized coordinates are represented, and the corresponding y _k [%] (k = 1,2, ... n) is used as the steepness measurement data.

X _k is an absolute coordinate with the width center of the material being “0”: X _k [mm] (k = 1,2, ... n) and the width of the material: W [m
m] and x _k = X _k / (W / 2). Also,
The steepness: y _k is n tension measurement values measured in the width direction: T _k [kg / mm] (k = 1, 2, ... N), and the maximum value thereof is T _max [ kg / mm] and σ _k = T _max −T _k [kg / mm], y _k = sqr [4 · 10 ⁴ · σ _k / π ² / E] [%] (where , Sqr [] represents the square root of []]. E is the Young's modulus of the target material.

Next, n data sets (x _k , y _k )
Using (k = 1,2, ... n), a fourth-order polynomial approximation that best fits these data sets by the least-squares method y = β ₀ + β ₁ · x + β ₂ · x ² + β ₃ · x ³ + β ₄ · x ⁴ (| x | ≦ 1) (1) is calculated.

[0008] Conventional shape evaluation method, the coefficient of the determined polynomial approximate expression: β ₁ ~β ₄ using, lambda ₁ to [lambda] _4, which is calculated by the conventional shape metrics derived matrix equation (2) Is a method using.

[0009]

[Equation 2]

The method of adopting the shape evaluation index obtained by the equation (2) is currently generally used in the shape evaluation and control of a sheet rolling mill, but the method of deriving the matrix coefficient of the equation (2) is a simple method. Since it is lacking in rigor, the following practical problems have been pointed out. The problems are listed below.

(1) Λ _{1 to} Λ ₄ do not correspond well to the characteristics of the shape; the shape of the material produced in the actual production process is typically U (or ∩, W, M, /, \, N). , Left / right inverted N
, Λ ₁ to Λ ₄ do not have corresponding values. When the shape evaluation index is applied in the actual production process, it is an essential condition that a typical shape abnormality can be intuitively grasped by the magnitude of the value, but this is not satisfied.

(2) A more complicated shape cannot be evaluated;
When the fourth-order polynomial approximation is insufficient, it is necessary to approximate to a sixth-order or higher-order polynomial for evaluation or control, but the conventional simple method is difficult to handle. In particular, the 6th-order shape evaluation is required in response to the improvement of the detection accuracy of the shape detection device and the sophistication of the shape control actuator, but it is extended to the 6th or higher order shape evaluation method. Can not do it.

[0013]

As described above, in the conventional shape evaluation method, the conversion method from the coefficients of the polynomial approximation formula: β _{1 to} β ₄ to the shape evaluation index: Λ ₁ to Λ ₄ is simple. Therefore, there was a problem in practical use. The desirable characteristics of the new index to leave proposed in place of conventional shape metrics listed below: (1) Λ (the fourth-order when lambda ₁ to [lambda] _4, 6-order when lambda ₁ ~
Λ ₆ ) can represent the shape of each product produced in the actual production process as a typical shape corresponding to its order, (2) if necessary, based on the same idea,
It is possible to derive an evaluation index of order 8 or higher, and it is possible to express even more complicated shapes. (3) Shape evaluation planes (or spherical surfaces, hereinafter referred to as "planes") of symmetric and asymmetric components In this case, when the evaluation index is plotted on 3D coordinates), the feature of the shape can be read from the vector length and phase, and (4) the conventional method applied in the secondary processing step. It should be an evaluation index that is applicable to the method of evaluating the maximum steepness based on the pitch by measuring the maximum wave height by placing a cutting plate on the surface plate, which is the evaluation method of.

The present invention solves the above-mentioned conventional problems,
An object of the present invention is to provide a thin plate shape evaluation method that can perform shape evaluation correctly, provide appropriate evaluation data when performing shape control based on this evaluation index, and eventually improve product quality assurance accuracy.

[0015]

As described above, the calculation method of the shape evaluation index of the present invention for solving the above-mentioned problems is as follows. First, n steepness in the width direction measured by the shape detecting device is used. (1) or (3) as before using the measurement data
It is approximated to a fourth-order or sixth-order polynomial shown by the formula.

Y = β ₀ + β ₁ · x + β ₂ · x ² + β ₃ · x ³ + β ₄ · x ⁴ + β ₅ · x ⁵ + β ₆ · x ⁶ (3) Next, the equivalent peak value is constant. Derived under the condition
The shape evaluation index: Λ _{1 to} Λ ₄ or Λ _{1 to} Λ ₆ is calculated using the conversion formula from β to Λ composed of the formula (4) or the formula (5).

[0017]

[Equation 4]

The calculated Λ is divided into a symmetric component consisting of only even-order terms and an asymmetric component consisting of only odd-order terms, and each is plotted on the symmetric component evaluation plane and the asymmetric component evaluation plane to evaluate the shape.

Next, the concept of deriving the coefficients of the shape evaluation index calculation matrix will be described. The condition that the equivalent peak value is constant is that the shape is regarded as a sine wave or its composite wave, and the following relational expression (6) is established between the effective value: y _{rms of the} function expressing the shape and the peak value: y _pp. Shall be established.

Y _rms = y _pp / 2 / sqr [2] (6) As a result, it can be associated with the maximum steepness that is conventionally used in the manufacturing site as a shape evaluation method. Also,
From the viewpoint of shape control, since the shape control capability of the actuator can be represented by a sine wave or a composite wave thereof, the above conditions are practically appropriate prerequisites.

Further, regarding the conventional method of evaluating the shape by dividing it into a symmetric component and an asymmetric component, in the aspect of controlling the shape, the actuators to be adjusted are different between the symmetric component and the asymmetric component, and for correction. Other actions are different.

[0022]

[Operation] The derivation process of the shape evaluation index Λ will be described below. First, consider the symmetric component in the case of the fourth order. _Let y _even be the component consisting of even-order terms in the polynomial approximation formula,
It becomes formula (7).

Y _even = β ₂ · x ² + β ₄ · x ⁴ (7) The average value of y _even : y _eave is obtained, and by using this, the square value of the effective value: y _erms ² Ask for.

[0024] _{y eave = β 2/3 +} β 4/5 ··· (8) y erms 2 = (y even -y eave) 2 = 4/45 · β 2 2 +16/105 · β 2 · β 4 + 16 / 225 ・ β ₄ ² (9) _Assuming that the shape is approximately represented by a sine wave, the difference between the maximum and minimum values, that is, the peak value: y _epp and y _erms , is _expressed by equation (6). There is. From Eqs. (6), (8), and (9), Eq. (10) is obtained.

4/45 · β ₂ ² + 16/105 · β ₂ · β ₄ + 16/225 · β ₄ ² = 1/8 · y _epp ² (10) In FIG. ), The value of y _epp is 0.2, 0.
A graph showing the relationship between β ₂ and β ₄ at ₄ , 0.6, 0.8, and 1.0 is shown. As shown, approximately on beta _{2-beta 4} planes 42 [d
eg] The elliptical locus becomes inclined. The equation (10) is subjected to coordinate rotation by affine transformation to eliminate the cross term of β ₂ · β ₄ . When a new coordinate system and u _e -v _e coordinates, the equation (11).

[0026] ^{_{A e · v e 2 + B}} e · u e 2 = y epp 2 ··· (11) (11) In the ^{_{equation, A e = 2 5/5}} 2/3 2/7 · (28-60 · ^{_{ω e +35 · ω e 2)}} / (1 + ω e 2) B e = 2 5/5 2/3 2/7 · (35-60 · ω e +28 · ω e 2) / (1 + ω e 2) ω e = It is {−7 + sqr (3649)} / 60.

[0027] in FIG. 1 (b), equal RMS trajectory in u _e -v _e coordinate system after coordinate transformation, shown in front same condition.
The coordinate gain conversion is applied to the equation (11), and v _e = t _e / sqr
(A _e), v Substituting _{e = s e / sqr (B} e), a circle function shown in the new coordinate system to the s _e -t _e coordinates (12).

[0028] _{^{t e 2 + s e 2 =}} y epp 2 ··· (12) in FIG. 1 (c), in the s _e -t _e coordinate system, showing the trajectory when the same conditions as above. By rewriting s _e as Λ ₂ and t _e as Λ _4, and summarizing a series of conversion processes, formula (13) is obtained.

[0029]

(Equation 13)

[0030] Based on the same concept as symmetric element also when the asymmetric component, to convert into lambda ₁ 1-? ₃ coordinate system from beta _{1-beta 3} coordinates. The result of deriving the conversion formula is shown in Eq. (14).

[0031]

[Equation 14]

A combination of the equations (13) and (14) and represented by one equation is a shape evaluation index calculation matrix based on the method of the present method for the quaternary shown in the equation (4). .

2 (a) to 2 (c), an equivalent peak value in a series of conversion _processes of the asymmetric component: y _opp =
The graph showing the locus on each coordinate axis at 0.2, 0.4, 0.6, 0.8, and 1.0 is shown.

Next, a method of expressing a more complicated shape in the 6th order will be described as an example in the same way as the case of the 4th order. Assuming that the polynomial approximation formula of the shape is the 6th-order (3) formula, the symmetric component and the asymmetrical component are considered separately as in the case of the 4th-order.

Y = y _even + y _odd (15) y _even = β ₂ · x ² + β ₄ · x ⁴ + β ₆ · x ⁶ y _odd = β ₁ · x + β ₃ · x ³ + β ₅ · x ⁵ First , The conversion process from β to Λ for the symmetric component will be shown in order following the above example. 1) Mean value: y _Eave and 2 rms squared: calculation of y _ERMS ² (formula (16), (17)) y eave = β 2/3 + β 4/5 + β 6/7 ··· (16) y _erms ² = 4/45 ・ β ₂ ² ＋16/225 ・ β ₄ ² ＋36/637 ・ β ₆ ² ＋16/105 ・ β ₂・ β ₄ ＋48/385 ・ β ₄・ β ₆ ＋24/189 ・ β ₆・ β ₂ = 4/45 ・ X _e ² ＋16/225 ・ Y _e ² ＋36/637 ・ Z _e ² ＋16/105 ・ X _e・ Y _e +48/385 ・ Y _e・ Z _e +24/189 ・ Z _e・ X _e ... (17). 2) _Derivation of the relational expression between β ₂ , β ₄ , β ₆ and y _epp (Equation (18))
Using the relationship of equation (6), a _e · β ₂ ² + b _e · β ₄ ² + c _e · β ₆ ² + d _e · β ₂ · β ₄ + e _e · β ₄ · β ₆ + _fe · β ₆ · β ^{_{2 = y epp 2 ··· (18}} ) _{where, a e = 4/45 ·} 8, b e = 16/225 · 8, c e = 36/637 · 8 d e = 16/105 · 8 e e = 48/385/8 _fe = 24/189/8.

3) Eliminating cross terms by three-dimensional affine transformation (Equation (19)) A _e · U _e ² + B _e · V _e ² + C _e · W _e ² = y _epp ² (19) where _{, A e = 4.264645, B e} = 0.267123, C e = 0.005
020.

4) Coordinate gain conversion R _e = 1 / sqr (A _e ), S _e = 1 / sqr (B _e ), T _e = 1 /
Substituting sqr (V _e ) into the equation (19), R _e ² + S _e ² + T _e ² = y _epp ² = Λ ₂ ² + Λ ₄ ² + Λ ₆ ² (20) 5) A series of conversion processes By replacing R _e with Λ ₂ , S _e with Λ ₄ , and T _e with Λ ₆ , the following (2
1) Obtain the formula.

[0038]

[Equation 21]

The asymmetric component is similarly calculated, and (2
2) Obtain the formula.

[0040]

[Equation 22]

The conversion matrix from β to Λ including the symmetrical and asymmetrical components is given by the equation (5). Hereinafter, the effects of applying the shape evaluation index according to the present invention will be described with reference to Examples based on comparison with a conventional method.

[0042]

[Embodiment] FIGS. 3 and 4 show a method (hereinafter referred to as a conventional method) based on the conventional simple shape evaluation index derivation expression based on the expression (2).
The four representative points (1,0), (0,1) on the unit circle on the symmetrical component plane (Λ ₂ −Λ ₄ plane) of the method according to the present invention (hereinafter referred to as the present method) according to the equation (4), (-1,0) and (0,-
The shape corresponding to 1) is illustrated. In FIGS. 3 and 4,
Since the output of the actual shape detection device is a discrete value, xn (normalized width coordinate) was divided into 40 equal parts in order to make a correspondence with this on the image. The features of the method of the present invention in comparison with the conventional method are listed below.

1) At Λ ₄ = 0, only Λ ₂ has a point (1, 0),
Shape at (-1, 0) The conventional method (Fig. 3) represents a composite shape of U type and W type or a combination of ∩ type and M type. Indicates.

2) When Λ ₂ = 0, only the point (0, 1) of Λ ₄ ,
Shape at (0, -1) In the conventional method, the shape at (0, 1) is M-shaped, but in this method it is W-shaped, which corresponds to the shape that the Λ ₄ axis should originally represent. Since this is reversed in the conventional method, it sometimes causes confusion on the side of utilizing the evaluation index.

3) Effective value Although the values at the above-mentioned four points are not constant in the conventional method, they are constant values in this method, y _rms = 0.35 [%] in this example. Although not shown in the figure, this is more prominent at points other than the four points and the asymmetric component.

4) Peak value As far as these four points are concerned, in the conventional method, y _pp is almost "1".
However, it does not become "1" by this method. Although not shown, the conventional method has a larger difference from “1” in consideration of points other than four points and an asymmetric component. In this method, the equivalent peak value described above is constant.

From the above four points, and even when the inventors applied the evaluation method according to the present method to the shape detection system of an iron temper rolling mill, the present method correctly evaluates the actual shape. It was confirmed.

FIG. 5 shows the actual rolled shape plotted on the Λ ₂ -Λ ₄ plane with this system. Figure 5
5A shows the result evaluated by the conventional method, and FIG. 5B shows the result evaluated by the present method. The main shape is U-shape or ∩-shape, which is the most popular shape in the actual production process. In the conventional method, Λ ₄ is evaluated as having a complex shape, but in the new method, it is estimated that the shape is mainly composed of Λ ₂ components. Although the shape correction operation (the target shape is flat in this example) is performed based on the evaluation result, the target flat shape could not be achieved by the conventional method. Next, evaluation of more complicated shapes will be described.

FIG. 6 is an example in which the present inventors applied the present method to a shape detection system of an actual iron Sendzimer rolling mill.
FIG. 6 (a) shows the steepness value measured online by the shape detection device and the shape obtained by cutting off the relevant site offline and measuring the steepness strictly using the displacement meter on the surface plate. is there. White circles indicate offline data and black circles indicate online data. Further, the number of tension distribution sensors is 32, and the number of effective points is 24 in this example. Data points are connected by straight lines. The horizontal axis indicates the position corresponding to the sensor position as "Sensor No.", x indicates the actual dimension in the plate width direction, and xn indicates the normalized plate width. From FIG. 6 (a), it was confirmed that the shape measured by this shape detection device corresponds well to the strict shape measured offline, and has sufficient accuracy to be applied to the subsequent shape evaluation. There is. In general, the offline measurement value and the online measurement value do not completely match because the measurement methods are different, and one is a cutting plate and the other is a continuous strip.

Online data and offline data, respectively, subjected to fourth-order, sixth-order, and eighth-order polynomial approximation by this method are shown in FIGS. 6 (b) and 6 (c). . Both online (FIG. 6 (b)) and offline data (FIG. 6 (c)) show almost the same tendency, but here it is listed below that the fourth-order shape evaluation is insufficient.

1) Approximation accuracy In FIGS. 6 (b) and 6 (c), the white circles represent the measured values, the broken line is the fourth order, the solid line is the sixth order, and the dotted line is the eighth order. Indicates. As you can see from the figure, 4
The following approximation does not provide sufficient approximation accuracy. Also,
There is almost no significant difference between the 6th order and the 8th order, and it can be seen that the 6th order is sufficient in this application example.

2) Shape evaluation of edge part The edge part is recognized as a downward shape when approximated in the fourth order, but is recognized as an upward shape in the sixth order.

3) Shape evaluation near edge In the fourth order evaluation, the actual shape and its differential value, that is, the tendency of change are reversed. The 6th order correctly evaluates the tendency.

From the above, it is understood that shape evaluation of a sixth order or higher is necessary for evaluation of a shape rolled by a rolling mill having split backup rolls such as a Zenzimer rolling mill. In particular, the shape evaluation of 2) above is important in actual rolling work, and if it is recognized as the 4th order and the control is performed based on this, the rolled material will be broken during rolling. It causes serious trouble in operation.

[0055]

As described above, the shape evaluation method according to the present invention is superior to the conventional method with reference to the embodiments. It was obtained by applying this method to an actual iron shape detection system. The effects will be described below.

1) The conventional shape evaluation method could not correctly recognize the features of the thin plate shape produced in the actual production process.
By using this method, it became possible to correctly evaluate the actual rolled shape. As a result, the shape correction action based on the shape evaluation index was correctly performed, and the productivity was improved.

2) In the conventional method, the complicated shape as described above could not be evaluated and linked to the corrective action, but by applying the method of the present invention, the higher-order shape evaluation is performed and the action is performed based on it. The product shape has been improved and complaints from the next process or customers have decreased. In addition, the shape of the edge part was evaluated correctly and actions based on this were taken, resulting in a reduction in operational troubles such as breakage of the plate during rolling.

3) Since the shape can be correctly evaluated, the concept of the equivalent peak value is introduced, and the shape is a sine wave or a composite wave thereof, which is an evaluation index in consideration of shape control. , It becomes possible to effectively use it when testing and analyzing which of the actuators has what performance and how much for the shape correction control. In the past, Λ did not represent a typical shape, so the method of calculating the influence coefficient used for performance evaluation was complicated.

[Brief description of drawings]

FIG. 1 (a) is a graph in which a coefficient β ₂ of a quadratic term and a coefficient β _{4 of a} quartic term, which are symmetric components, of a quartic polynomial approximation expression representing steepness calculated from a tension measurement value are coordinates β ₂ Equivalent peak values on the −β ₄ plane are 0.2, 0.4, 0.6, 0.8, 1.0
3 is a graph showing a locus of In (b), the graph shown in (a) is subjected to affine transformation to obtain a new coordinate system u-v.
6 is a graph showing the result of rotating the coordinates as and converting to a regular ellipse. (C) is a graph in which a ov coordinate system is subjected to gain conversion to convert a regular ellipse into a perfect circle and is represented by coordinates s-t (Λ ₂ −Λ ₄ ).

FIG. 2 (a) is a graph showing a steepness calculated from a tension measurement value, which is asymmetrical, and whose first-order term coefficient β ₁ and third-order term coefficient β ₃ are β ₁ as coordinates. −β ₃
It is a graph which shows the locus of the equivalent peak value in a coordinate system. (B) is a graph showing a result obtained by performing affine transformation on the graph shown in (a), rotating the coordinate with a new coordinate system being u-v, and converting the graph into a regular ellipse. (C) is uv
7 is a graph in which a coordinate transformation is performed on a coordinate system, a regular ellipse is transformed into a perfect circle, and the coordinate is represented by coordinates st (Λ ₁ −Λ ₃ ).

FIG. 3 is a bar graph showing the shape at four characteristic points on the Λ ₂ −Λ ₄ plane ((c) of FIG. 1) of the conventional method, and in the four bar graphs showing the shape, the horizontal axis is the normalized coordinate:
x _n , the vertical axis is steepness: y [%], and the x _n axis is divided into 40 equal parts, which corresponds to the number of sensors of the shape detection device. Conventionally, in shape evaluation, the material is placed on a surface plate and the rising height of the material is measured.

FIG. 4 is a bar graph showing the shape at four points as in the case of FIG. 3 according to the method of the present invention.

FIG. 5 is a graph in which the shape evaluation index of the actual shape measurement data is calculated by the conventional method and this method, and the result is plotted on the symmetric component plane (Λ ₂ −Λ ₄ ), and the number of data points is 4 respectively.
It is the same as the original shape data at 0 points. (A) shows the result by the operation of the conventional method, and (b) shows the result by the operation of the method of the present invention.

FIG. 6 is a graph showing an actually measured polynomial approximation result of a complex shape, showing a difference in approximation accuracy due to a difference in order.
(A) is a graph in which original raw data before polynomial approximation is plotted, and white circles represent offline measurement data and black circles represent online measurement data. It is shown to show that the shape detector data has sufficient performance that requires rigorous analysis. (B) is a graph showing a curve obtained by approximating the measurement shape using the on-line measurement data, which is a fourth-order, sixth-order, and eighth-order polynomial. (C) is a graph showing a curve obtained by approximating a measurement shape with a fourth-order, sixth-order, and eighth-order polynomial using offline measurement data. (B)
In (c), a thick solid line represents a sixth-order curve, a broken line represents a fourth-order curve, and a thin solid line represents an eighth-order curve in a polynomial approximation formula. The horizontal axis is the width direction coordinate of the material, the width direction center is "0",
It is displayed. The sensor positions are numbered 1-32. The vertical axis represents steepness.

Claims (1)

[Claims] The shape of the thin plate measured by the shape detection device is converted into a plurality of feature quantities and plotted on the shape evaluation plane or spherical surface for each of the symmetric and asymmetric components, and the shape is evaluated by the vector length and phase. When steepness measurement data is approximated to a curve with a polynomial of 4th order or higher and the shape evaluation index is calculated and derived from the coefficient of the approximate expression, when the shape is regarded as a sine wave or a composite wave including its higher order components The peak value of the shape viewed from the relationship between the peak value and the effective value is defined as the equivalent peak value, and the shape is converted so that the locus of points on the above-mentioned plane or spherical surface where the equivalent peak value is constant becomes a circle or a sphere. An evaluation method of a thin plate shape, which has a calculation derivation formula to an evaluation index.